Matches in SemOpenAlex for { <https://semopenalex.org/work/W2951985129> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2951985129 abstract "This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability distributions on a state space, defined so that it corresponds to the maximum possible entropy given known observed statistical averages, although non-classical entropy-like objective functions will also be considered. First the set of admissible moments must be established, and under the conditions presented in this work the set is open, bounded and convex allowing a description in terms of supporting hyperplanes, which provides estimates on the development of singularities for related probability distributions. Under appropriate conditions it is shown that the singular potential is strictly convex, as differentiable as the microscopic entropy and blows up uniformly as the macroscopic variable tends to the boundary of the set of admissible moments. Applications of the singular potential are then discussed, and particular consideration will be given to certain free-energy functionals typical in mean-field theory, demonstrating an equivalence between certain microscopic and macroscopic free-energy functionals. This allows statements about L^1-local minimisers of Onsager's free energy to be obtained which cannot be given by two-sided variations, and overcomes the need to ensure local minimisers are bounded away from zero and infinity before taking bounded variations. The analysis also permits the definition of a dual order parameter for which Onsager's free energy allows an explicit representation. Also the difficulties in approximating the singular potential by everywhere defined functions, in particular by polynomials, are addressed with examples demonstrating the failure of the Taylor approximation to preserve shape properties of the singular potential." @default.
- W2951985129 created "2019-06-27" @default.
- W2951985129 creator A5065057468 @default.
- W2951985129 date "2015-02-23" @default.
- W2951985129 modified "2023-09-27" @default.
- W2951985129 title "Maximum entropy methods as the bridge between macroscopic and microscopic theory" @default.
- W2951985129 cites W1517022795 @default.
- W2951985129 cites W1517823887 @default.
- W2951985129 cites W1518472176 @default.
- W2951985129 cites W1537639429 @default.
- W2951985129 cites W1576301438 @default.
- W2951985129 cites W1582617215 @default.
- W2951985129 cites W1884347414 @default.
- W2951985129 cites W1967391867 @default.
- W2951985129 cites W1970215649 @default.
- W2951985129 cites W2000148092 @default.
- W2951985129 cites W2020084878 @default.
- W2951985129 cites W2032558547 @default.
- W2951985129 cites W2037120273 @default.
- W2951985129 cites W2058430348 @default.
- W2951985129 cites W2066875242 @default.
- W2951985129 cites W2079990553 @default.
- W2951985129 cites W2096876265 @default.
- W2951985129 cites W2169280780 @default.
- W2951985129 cites W2314782808 @default.
- W2951985129 cites W2949476993 @default.
- W2951985129 cites W2950367984 @default.
- W2951985129 cites W2963613067 @default.
- W2951985129 hasPublicationYear "2015" @default.
- W2951985129 type Work @default.
- W2951985129 sameAs 2951985129 @default.
- W2951985129 citedByCount "2" @default.
- W2951985129 countsByYear W29519851292016 @default.
- W2951985129 countsByYear W29519851292017 @default.
- W2951985129 crossrefType "posted-content" @default.
- W2951985129 hasAuthorship W2951985129A5065057468 @default.
- W2951985129 hasConcept C105795698 @default.
- W2951985129 hasConcept C106301342 @default.
- W2951985129 hasConcept C121332964 @default.
- W2951985129 hasConcept C121864883 @default.
- W2951985129 hasConcept C12843 @default.
- W2951985129 hasConcept C134306372 @default.
- W2951985129 hasConcept C21031990 @default.
- W2951985129 hasConcept C33923547 @default.
- W2951985129 hasConcept C34388435 @default.
- W2951985129 hasConcept C62520636 @default.
- W2951985129 hasConcept C9679016 @default.
- W2951985129 hasConceptScore W2951985129C105795698 @default.
- W2951985129 hasConceptScore W2951985129C106301342 @default.
- W2951985129 hasConceptScore W2951985129C121332964 @default.
- W2951985129 hasConceptScore W2951985129C121864883 @default.
- W2951985129 hasConceptScore W2951985129C12843 @default.
- W2951985129 hasConceptScore W2951985129C134306372 @default.
- W2951985129 hasConceptScore W2951985129C21031990 @default.
- W2951985129 hasConceptScore W2951985129C33923547 @default.
- W2951985129 hasConceptScore W2951985129C34388435 @default.
- W2951985129 hasConceptScore W2951985129C62520636 @default.
- W2951985129 hasConceptScore W2951985129C9679016 @default.
- W2951985129 hasLocation W29519851291 @default.
- W2951985129 hasOpenAccess W2951985129 @default.
- W2951985129 hasPrimaryLocation W29519851291 @default.
- W2951985129 hasRelatedWork W1518554152 @default.
- W2951985129 hasRelatedWork W1611502116 @default.
- W2951985129 hasRelatedWork W1777675546 @default.
- W2951985129 hasRelatedWork W1979987326 @default.
- W2951985129 hasRelatedWork W2000705786 @default.
- W2951985129 hasRelatedWork W2070152166 @default.
- W2951985129 hasRelatedWork W2098282686 @default.
- W2951985129 hasRelatedWork W2111450510 @default.
- W2951985129 hasRelatedWork W2603041447 @default.
- W2951985129 hasRelatedWork W2810394586 @default.
- W2951985129 hasRelatedWork W2884177155 @default.
- W2951985129 hasRelatedWork W2901215682 @default.
- W2951985129 hasRelatedWork W2937179554 @default.
- W2951985129 hasRelatedWork W2950848449 @default.
- W2951985129 hasRelatedWork W2951227043 @default.
- W2951985129 hasRelatedWork W3010131193 @default.
- W2951985129 hasRelatedWork W3042626547 @default.
- W2951985129 hasRelatedWork W3098290291 @default.
- W2951985129 hasRelatedWork W3100132315 @default.
- W2951985129 hasRelatedWork W2409057605 @default.
- W2951985129 isParatext "false" @default.
- W2951985129 isRetracted "false" @default.
- W2951985129 magId "2951985129" @default.
- W2951985129 workType "article" @default.